Nikhil spent 20% of his monthly income on food and 15% on house rent. 40% of the remaining he spent on trasport and 30% on entertainment. He is left with an amount of Rs. 8775 after all the expenditures. What is Nikhil's monthly income?

Options

A. A)Rs.40000
B. B)Rs.45000
C. C)Rs.48000
D. D)Rs.54000

Answer

To solve the problem step by step, we will first define Nikhil's monthly income and then calculate his expenditures based on the percentages given. Finally, we will find his total monthly income based on the amount he has left after all expenditures.

### Step-by-Step Solution:

1. **Define Nikhil's Monthly Income:**
Let's assume Nikhil's monthly income is represented as 100 units.

2. **Calculate Expenditure on Food:**
Nikhil spends 20% of his income on food.
\[ \text{Expenditure on Food} = 20\% \text{ of } 100 = 20 \text{ units} \]

3. **Calculate Expenditure on House Rent:**
Nikhil spends 15% of his income on house rent.
\[ \text{Expenditure on House Rent} = 15\% \text{ of } 100 = 15 \text{ units} \]

4. **Calculate Remaining Income After Food and Rent:**
After spending on food and house rent, the remaining income is:
\[ \text{Remaining Income} = 100 - (20 + 15) = 100 - 35 = 65 \text{ units} \]

5. **Calculate Expenditure on Transport:**
Nikhil spends 40% of the remaining income on transport.
\[ \text{Expenditure on Transport} = 40\% \text{ of } 65 = \frac{40}{100} \times 65 = 26 \text{ units} \]

6. **Calculate Expenditure on Entertainment:**
Nikhil spends 30% of the remaining income on entertainment.
\[ \text{Expenditure on Entertainment} = 30\% \text{ of } 65 = \frac{30}{100} \times 65 = 19.5 \text{ units} \]

7. **Calculate Remaining Income After All Expenditures:**
After all expenditures, the remaining income is:
\[ \text{Remaining Income} = 65 - (26 + 19.5) = 65 - 45.5 = 19.5 \text{ units} \]

8. **Relate Remaining Income to Given Amount:**
According to the problem, Nikhil is left with Rs. 8775 after all expenditures, which corresponds to 19.5 units.
\[ 19.5 \text{ units} = 8775 \text{ Rs.} \]

9. **Calculate Value of One Unit:**
To find the value of one unit, we divide the total amount by the number of units.
\[ \text{Value of One Unit} = \frac{8775}{19.5} = 450 \text{ Rs.} \]

10. **Calculate Nikhil's Monthly Income:**
Since we assumed Nikhil's monthly income to be 100 units, we can now calculate it in Rs.
\[ \text{Monthly Income} = 100 \text{ units} \times 450 \text{ Rs.} = 45000 \text{ Rs.} \]

### Final Answer:
Nikhil's monthly income is Rs. 45000.

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